A uniformly accurate collocation method for a singularly perturbed problem


Zorica Uzelac, Katarina Surla




A semilinear singularly perturbed reaction-diffusion problem is considered and the approximate solution is given in the form of a quadratic polynomial spline. Using the collocation method on a simple piecewise equidistant mesh, an approximation almost second order uniformly accurate in small parameter is obtained. Numerical results are presented in support of this result.